Question: $B$ is the midpoint of $\overline{AC}$ $A$ $B$ $C$ If: $ AB = 6x - 1$ and $ BC = 2x + 27$ Find $AC$.
Explanation: A midpoint divides a segment into two segments with equal lengths. ${AB} = {BC}$ Substitute in the expressions that were given for each length: $ {6x - 1} = {2x + 27}$ Solve for $x$ $ 4x = 28$ $ x = 7$ Substitute $7$ for $x$ in the expressions that were given for $AB$ and $BC$ $ AB = 6({7}) - 1$ $ BC = 2({7}) + 27$ $ AB = 42 - 1$ $ BC = 14 + 27$ $ AB = 41$ $ BC = 41$ To find the length $AC$ , add the lengths ${AB}$ and ${BC}$ $ AC = {AB} + {BC}$ $ AC = {41} + {41}$ $ AC = 82$